"남자는 화를 냈다."
Translation:A man got angry.
화가 났다 means that the anger came about or it occured, so "got angry" would be correct.
화를 냈다 is more like... when you release your anger. For example yelling or doing something because of your anger.
It's a small difference, but I can't think of a different way to comfortably say it in English except "got angry"